Dynamic Screening: Accelerating First-Order Algorithms for the Lasso and Group-Lasso

TL;DR

This paper introduces a dynamic screening method that accelerates first-order algorithms for Lasso and Group-Lasso by adaptively screening the dictionary during each iteration, leading to faster convergence and computational savings.

Contribution

It proposes a novel dynamic screening approach that integrates screening tests within each iteration of regression algorithms, improving efficiency over static screening methods.

Findings

Significant reduction in computational time on synthetic and real data.

Enhanced screening effectiveness with increasing iteration-based screening.

Applicable to various first-order algorithms for sparse regression.

Abstract

Recent computational strategies based on screening tests have been proposed to accelerate algorithms addressing penalized sparse regression problems such as the Lasso. Such approaches build upon the idea that it is worth dedicating some small computational effort to locate inactive atoms and remove them from the dictionary in a preprocessing stage so that the regression algorithm working with a smaller dictionary will then converge faster to the solution of the initial problem. We believe that there is an even more efficient way to screen the dictionary and obtain a greater acceleration: inside each iteration of the regression algorithm, one may take advantage of the algorithm computations to obtain a new screening test for free with increasing screening effects along the iterations. The dictionary is henceforth dynamically screened instead of being screened statically, once and for all, before the first iteration. We formalize this dynamic screening principle in a general algorithmic scheme and apply it by embedding inside a number of first-order algorithms adapted existing screening tests to solve the Lasso or new screening tests to solve the Group-Lasso. Computational gains are assessed in a large set of experiments on synthetic data as well as real-world sounds and images. They show both the screening efficiency and the gain in terms running times.